Question: Solve for $x$ and $y$ using elimination. ${4x+3y = 40}$ ${-5x-3y = -44}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $3y$ and $-3y$ cancel out. $-x = -4$ $\dfrac{-x}{{-1}} = \dfrac{-4}{{-1}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {4x+3y = 40}\thinspace$ to find $y$ ${4}{(4)}{ + 3y = 40}$ $16+3y = 40$ $16{-16} + 3y = 40{-16}$ $3y = 24$ $\dfrac{3y}{{3}} = \dfrac{24}{{3}}$ ${y = 8}$ You can also plug ${x = 4}$ into $\thinspace {-5x-3y = -44}\thinspace$ and get the same answer for $y$ : ${-5}{(4)}{ - 3y = -44}$ ${y = 8}$